Abstract
We give a new construction of the outer automorphism of the symmetric group on six points. Our construction features a complex Hadamard matrix of order six containing third roots of unity and the algebra of split quaternions over the real numbers.
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Acknowledgements
Work on this paper was begun while the second author was visiting the Centre for the Mathematics of Symmetry and Computation at the University of Western Australia in March 2012. The hospitality of the CMSC is gratefully acknowledged, and in particular support from the ARC Federation Fellowship Grant FF0776186 of the third author, which also supported the first author. The second author acknowledges the support of the Australian Research Council via grant DP120103067, and Monash University where much of this work was completed. This research was partially supported by the Academy of Finland (Grants #276031, #282938, #283262 and #283437). The support from the European Science Foundation under the COST Action IC1104 is also gratefully acknowledged.
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Gillespie, N.I., Ó Catháin, P. & Praeger, C.E. Construction of the Outer Automorphism of \({\mathcal {S}}_{6}\) via a Complex Hadamard Matrix. Math.Comput.Sci. 12, 453–458 (2018). https://doi.org/10.1007/s11786-018-0382-0
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DOI: https://doi.org/10.1007/s11786-018-0382-0